The best first step to solve equations, x+y = 3 and 4x-y = 7, is to add the first equation to the second equation.
According to the question,
We have the following system of equations:
x+y = 3 .....(1)
4x-y = 7 ....(2)
Now, these equations can be easily solved by adding the first equation to the second equation because we will only then have one variable which is x and y when added to -y will result in zero.
We can solve these equations by adding as follows:
x-y+4x+y = 3+7
5x = 10
x = 10/5
x = 2
Now, we can put the value of x in equation 1 to find the value of y:
2+y = 3
y = 3-2
y = 1
Hence, the correct option is B.
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What is the slope of the line passing through the points (2, 4) and (5, 6)?
A. 6/11
B. -2/3
C. 7/10
D.2/3
Answer:
D, 2/3
Step-by-step explanation:
Using the Slope formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] we can find the slope of the line.
Input values:
[tex]m=\frac{6-4}{5-2}=\frac{2}{3}[/tex]
[tex]m=\frac{2}{3}[/tex]
Please help I’ve been stuck on this question for awhile thanks:)
Does anyone know how to do this?
The length of BC is 50 miles (approx).
What is Trigonometry?
Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.
Solution:
In the triangle ABC,
The perpendicular = BC
The Base = AB = 6 miles
by using the trigonometric ratio "tan"
tan (58) = BC / AB
8.33 = BC / 6
49.98 miles = BC
BC = 50 miles (approx)
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A spinner is spun 800 times.
The probabilities it lands on each colour
are shown below.
The probability it lands on red is the same
as the probability it lands on yellow.
Colour Red Green Brown Yellow
Probability. 0.3. 0.54
How many times would you expect it to
land on each colour?
Red: 0
Brown: Yellow:
O
Green:
0
Answer:
green 45 times or 40 a note
find the Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ]
The Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ] is ( 5/√2, -5/√2)
The polar cordinates given are (r,θ)=(5,− π/4)
And we need to find the cartesian coordinates
We have,
x=rcosθ, y=rsinθ
x=5cos(− π/4) ,y=5sin(− π/4)
x= 5/√2 ,y=− 5/√2
So, the cartesian form is ( 5/√2, -5/√2)
The Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ] is ( 5/√2, -5/√2)
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The Monty Corporation has a staff of sales people who are paid a monthly salary of $1,600.00 plus an incremental commission based on the table below. If Sally sells $29,700.00, what is her total gross pay for the month
Answer:
Step-by-step explanation:
-28,100 if you subtract 29,700.00 - 1,600.00 = -28,100
Change 4 1/6to an improper fraction.
Answer:
4 1/6 = 25/6
Why?:
Multiply the denominator with the mixed number 4.
Add the numerator 1 and get 25.
Then, you keep the denominator (Which is 6) on the bottom.
And finally, you get
25/6
Answer:
25/6
Step-by-step explanation:
first start by multiplying 6 and 4, which leads you to 24
then add the 1 from the numerator and you get 25 as your numerator.
for the denominator, leave six as it is so it becomes 25/6
A cube has an edge measuring 7 inches.
What is the volume of the cube, in inches?
The third grade teachers had a pizza party. They ordered 11 large pizzas and each pizza had 8 slices. There were 4 classrooms in the grade. Estimate how many slices of pizza each classroom can have if the pizzas are shared equally.
Choose 1 answer: 20 slices 50 slices 300 slices 320 slices
Answer:
20 slices
Step-by-step explanation:
If there were 11 large pizzas with 8 slices per pizza, that would mean that there are a total of 88 slices of pizza.
If there are four classrooms, that means that if each classroom had 20 slices, there would be enough for everyone with 8 pieces leftover.
20 x 4 = 80
The hire purchase price of a refrigerator is $6509.A deposit of $500 is made and the reminder is paid in equal monthly payments of $250. Calculate the number of monthly payments that must be made.
Step-by-step explanation:
The hire purchase price of a refrigerator is $6509.A deposit of $500 is made and the reminder is paid in equal monthly payments of $250. Calculate the number of monthly payments that must be made.
amount paid over x months:
$6509 - $500 = $6,009
Equal payments of $250:
$6,009 / $250 = 24.036 months of payments
[Depending on if they want the answer rounded up, answer may become 25]
Answer:
hire purchase= $6509
deposit=$500
monthly payment=$250
no of monthly payment that must be made=hire purchase - deposit divided by monthly payment
$6509-$500/$250=$6009/$250= 24.036 month
At the beginning of a journey, the fuel tank of a car was 34 full. When the car reached its destination, it had consumed 60% of the gasoline in the tank. The full capacity of the fuel tank was w gallons.
a Enter an algebraic expression for the amount of gasoline left in the fuel tank.
gal
b If w = 15.5, how much gasoline was left in the tank at the end of the journey?
gal
a) An algebraic expression for the gasoline left in the fuel tank is L = 0.4w.
b) If w = 15.5, the amount of gasoline left in the tank at the end of the journey was 6.2 gallons.
What is an algebraic expression?An algebraic expression is a mathematical statement that combines constants and variables together with mathematical operands.
The mathematical operands include addition, subtraction, division, multiplication, etc.
Let L = the amount of gasoline left
Let the full capacity of the fuel tank = w gallons
Gasoline consumed on the journey = 60% = 0.6
Equation:L = w - 0.6w
L = 0.4w
Solution:If w = 15.5
L = 0.4(15.5)
= 6.2 gallons
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line x is the perpendicular bisector of segment ZY
what does YT equal
Answer:
Step-by-step explanation:
ZT=YT
x+3=3x-11
x-3x=-11-3
-2x=-14
x=-14/-2=7
YT=3×7-11=21-11=10
YT=10
Keiko tracks the change in outside
one afternoon. She records
temperature
a temperature of 85.4°F at noon. The
temperature rises 3.85°F over the
next 4 hours. At 5:00 PM, Keiko records
a temperature of 89.25°F. How does the
temperature change between
4:00 PM
and 5:00 PM?
Answer:
no change
Step-by-step explanation:
Given a temperature rise of 3.85 °F over 4 hours after noon, when the temperature is 85.4 °F, you want to know the change between 4 pm and 5 pm if the temperature at 5 pm is 89.25 °F.
Temperature at 4The temperature at 4 pm is the sum of the noon temperature and the change in the 4 hours after noon:
85.4 °F + 3.85 °F = 89.25 °F
Change after 4The change from 4 pm to 5 pm is the difference between the 5 pm temperature and the 4 pm temperature:
82.25 °F -89.25 °F = 0 °F
There is no change in the temperature between 4 pm and 5 pm.
Jacob held different part-time jobs during his summer holiday. The table below shows the total money he earned for different amounts of time, in hours.
What type of association will the scatter plot for this data represent between the number of hours worked and the total money earned?
1. A positive nonlinear association
2. A positive linear association
3. A negative nonlinear association
4. A negative linear association
Given the table on the total money earned, the type of association the scatter plot would represent is 2. A positive linear association
What is a positive linear association?When two variables are said to have a positive linear association, it means that they move in the same direction together. When one of them increases, the other increases as well. It also means that they are increasing by a uniform amount. For instance, when one variable increases by 3, the other increases by 6, always.
The hours worked here are increasing as well as the money earned by Jacob. The hours worked is increasing by 1, and the money earned is increasing by 4. This is therefore a positive linear association.
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A bank found that 2.5% of its loans to new small businesses become delinquent. If 400 small businesses are selected randomly from the bank’s files, what is the probability that at least 12 of them are delinquent? Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.
.3155
The probability that at least 12 are delinquent is given as 0.3155
How to solve for the probabilityProbability can be defined as the likelihood of getting an outcome out of other outcomes.
We have the mean u = np
where n = 400
p = proportion = 2.5% = 0.025
= 400 x 0.025
= 10
we have to find the population standard deviation
= [tex]\sqrt{np(1-p)}[/tex]
= √400 x 0.025 (1 - 0.025)
= 3.1225
P (X ≥ 12)
= P(X ≥ 11.5)
= 11.5 - 10 / 3.1225
= 1 - P(z < 0.4804)
= 1 - 0.6845
= 0.3155
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Simplify the experession
6²-3³)÷7
Answer:
9/7 or 1.285714
Step-by-step explanation:
Answer:9/7
Step-by-step explanation:
You want to have $300,000 when you retire in 30 years. If you can earn 4% interest compounded continuously, how much would you need to deposit now into the account to reach your retirement goal?
An amount of $ 92,495.60 must be the initial deposit to become into $ 300,000 by compound interest.
How much money must be deposited to obtain a given quantity for retirement?
In this problem we must determine the initial deposit that must become into $ 300,000 by compound interest after a period of 30 years. Compound interest model is a model where money gains interest continuously, whose formula is:
C' = C · (1 + r / 100)ⁿ
Where:
C - Initial deposit, in monetary units.C' - Final deposit, in monetary units. r - Interest rate, in percentage.n - Number of periods, in years.If we know that C' = 300,000, r = 4 and n = 30, then the initial deposit is:
C = C' / (1 + r / 100)ⁿ
C = 300,000 / (1 + 4 / 100)³⁰
C = 92,495.60
The initial deposit must be $ 92,495.60.
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8 (x + 2 ) when x = 6
Answer:
64
Step-by-step explanation:
8(x+2) when x=6
replace x with 6
8(6+2)
distribute 8
48+16= 64
The weight of substance X is halved per minute. In the beginning, the weight of substance X is 5kg.
(a) Find the weight of substance X after 4 minutes.
(b) After how many minutes will the weight of substance X first go below 0.5kg?
Please give your answer as an integer.
EMERGENCY PLEASE HELPPPP
Answer:
a: 0.3125kg
b: 4
Step-by-step explanation:
for a we simply calculate 5 * 0.5 ^ 4.
we then see that the weight after 4 minutes is smaller than 0.5kg, but if we go back to 3 minutes (by multiplying our solution to a by 2), giving us 0.625kg, which is now bigger than 0.5kg. meaning 4 minutes is the first whole amount that will give us a weight smaller than 0.5kg.
A relation contains the points (1,-4), (3, 2), (4, -3), (x, 7), and (-4, 6).
For which value of a will the relation be a function?
O-4
O-3
O 3
O 4%
For x = -3 the relation will be a function.
We know that a relation is a function when for each input there is exactly one output.
In this question, we need to find the value of x for which the relation will be a function.
We need to select the value of x such that x ≠ 1, 3, 4, -4
This means x must be -3
Therefore, For x = -3 the relation will be a function.
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Complete the chart to show similarities and differences between multiplying by 0.1, 0.01, 10, 100. Tell how many places the decimal point appears to move and in which direction when you multiply by each
Answer:
they all are being multiplied by 10
Step-by-step explanation:
0.01 x 10 = 0.1
0.1 x 10 = 1
1 x 10 = 10
10 x 10 = 100
What should be added to 5/6 to get 41/24
Answer: 26/24
Step-by-step explanation:
First we have to convert 5/6 with a denominator of 24 so 6 times what makes 24, that is 4 & whatever you do with the denominator, you have to do it with the numerator. So 5 times 4 is 20, the new fraction is 20/24. Now, we need to find what we need to add with 20/24 to get 41/24, so we subtract 20/24 from 41/24 & that is 21/24. We can check if it's correct by adding both 21/24 and 20/24 & that makes 41/24.
Which of the following examples would be continuous data?
How many people are late boarding an airplane?
The amount of diapers a newborn uses in a day.
The number of television shows on Netflix.
The volume of liquid in a pop can.
The example that would be continuous data is A. The volume of liquid in a pop can.
What is a continuous data?Continuous data is data that has no fixed value. Continuous data includes height, weight, temperature, and length. Some continuous data, such as a baby's weight in its first year or the temperature in a room throughout the day, will change over time.
Discrete data is a type of numerical data that consists of whole, concrete numbers that have specific and fixed data values determined by counting. Continuous data consists of complex numbers and varying data values measured over a specific time period.
In this case, the volume of the liquid is s continuous data.
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Solve the inequality for p
4 - 1/6 (p - 3) > 7
Answer:
p < -15
Step-by-step explanation:
[tex]4 - \frac{1}{6} (p - 3) > 7[/tex]
[tex] - \frac{1}{6} (p - 3) > 3[/tex]
[tex]p - 3 < - 18[/tex]
[tex]p < - 15[/tex]
4y-5x=3(4x-2y+1) in standard form
Answer:
7x+10y=3
Step-by-step explanation:
Standard Form= Ax+By=c
Distribute first
4y-5x=12x-6y+3
Add 6y
10y-5x=12x+3
Add 12x
7x+10y=3
Find the values of x and y.
Answer:
x = 20 degrees ; y = 70 degrees
Step-by-step explanation:
angle supplementary to 40 = 180 - 40 = 140 degrees
in isosceles triangle has the angles of the base with the same measure
140 + (2x) = 180
2x = 180 - 140
2x = 40
2/2 x = 40/2
x = 20 degrees
90 - 20 = 70 degrees
70 + y + 40 = 180
110 + y = 180
y = 180 - 110
y = 70 degrees
Answer:
Step-by-step explanation:
Find the mean, μ, for the binomial distribution which has
the stated values of n and p. Round answer to the nearest
tenth.
n = 38; p = 0.2
Select one:
Ο Α. μ = 8.3
OB. μ = 7.9
Cu = 7.1
OD. μ = 7.6
The mean value is 7.6. Option (D) is the correct answer.
The number of successes in a sample of size n drawn with replacement from a population of size N is frequently modeled using the binomial distribution.
The mean value of a binomial distribution is,
[tex]\mu =np\\=38*0.2\\=7.6[/tex]
Multiplication:
In mathematics, multiplying two or more numbers yields the product of the numbers. It is one of the basic mathematical operations that we carry out on a regular basis. The most obvious application is using multiplication tables. The multiplication of two numbers in mathematics represents the repeated addition of one number in respect to another. These numbers can be natural numbers, whole numbers, fractions, integers, or other types of numbers. When m is multiplied by n, m is either multiplied by n times or added to itself n times.
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What is the volume of a cylinder, in cubie centimeters, with a height of 2 centimeters
and a base diameter of 20 centimeters? Round to the nearest tenths place?
The volume of the cylinder in cubie centimeter is 628 [tex]cm^{3}[/tex]
How to find the volume of cylinder?
1. Find the radius of the circular base: Since both circles are the same size, either one will work. Move on if you are aware of the radius. If you don't know the radius, you can divide the diameter of the circle by 2.
2. Find the height of the cylinder : Continue if you already know the height. Otherwise, measure it with a ruler. The height is determined by the separation of the two bases' edges.
diameter (d) = 20
radius = [tex]\frac{20}{2}[/tex]
r = 10
height (h) = 2cm
volume v = [tex]\pi r^{2} h[/tex]
v = 3.14(10*10)2
= 628 [tex]cm^{3}[/tex]
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Identify the domain and range of the relation, and determine whether the relation is a function.
{(0, 3),(-1/3,0),(-5, 2),(1/3,4)}
How do I factor 250n2 + 20n8?
Step-by-step explanation:
[tex]250n^2+20n^8[/tex]
common factor is [tex]10n^2[/tex]:
[tex]10n^2(25 +2n^6)[/tex]
rearrange:
[tex]10n^2(2n^6+25)[/tex]
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
Answer:
A
Step-by-step explanation:
